GMAT Data Sufficiency: General or Specific?

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Whether you've taken a prep course or not, odds are you've learned (or have figured out) a method for Data Sufficiency something like trial and error. You pick some numbers, assign them to variables, and see if they work. You figure out what they tell you about the sufficiency of the statements, and you are spared the difficulty and complexity that sometimes comes with really thinking through the problem.

It's a useful method, one that I advocate for some questions. However, assigning values to variables is only useful if you apply it with care: while you're working with a specific number, you need to think about the general implications. If x = 4, will you get the same results you would for all values of x? All positive values of x? All evens? All perfect squares? You usually won't have time to try every possible value for each variable, so you must think abstractly.

To give you a better idea of what I mean, let's look at a sample question, DS question #112 from page 287 of the Official Guide to GMAT Review:

Is k greater than t?

(1) kt = 24

(2) k^2 > t^2

Most people approach this question by trying a few values for k and t and seeing if a rule emerges. An edited version of that thought process might look like this:

(1) If k is 8, then t is 3...but if k is 4, then t is 6. Insufficient.

(2) If k is 6, t could be 4...but if k is -6, t could still be 4. Insufficient.

Taken together: k and t could be 8 and 3, but not 4 and 6, because of (2). k and t could be 6 and 4, but not -6 and 4, because of (1). Looks like they are sufficient, taken together. The answer is (C).

If you're a step ahead of me, congratulations: you know that the answer is really (E), because k and t could be -6 and -4, respectively, which makes t the greater quantity. Sometimes, when I explain this sort of thing to students in person, they start thinking they'll never figure it out: how do you know what numbers to pick, and when you don't have to pick any more numbers?

To full answer that question would require another tip, but thinking in more general terms will often help avoid such pitfalls. Instead of listing as many possible values as you can, find one or two, and think about how much that number tells you. Here's how you might think about statement (2) above:

(2) k^2 > t^2

If k is 6, t could be fact, any time both numbers are positive, k must be bigger than t. But, I know the GMAT likes to see if I'm thinking about negatives, so what about those? If k is negative, t could be either positive or negative, as long as the square of t is smaller than square of k. Actually, I can use the same numbers I used before, only negative: if k is -6, t could be -4. If both numbers are number, k must be smaller than t.

See the difference? The latter method of thinking may feel more cumbersome (especially at first, if it doesn't come naturally to you), but you'll rarely have to think of more than one or two sets of values for each statement. Not only that, but those sets of values will tell you more than what you've been learning from 3 or more sets using the first method of thinking.

Picking numbers is a great strategy: just don't turn off your brain when you start to apply it. View each set of values as a case study with far-reaching implications, and Data Sufficiency questions that once sent your head reeling will be well within your grasp.



About the author: Jeff Sackmann has written many GMAT preparation books, including the popular Total GMAT Math, Total GMAT Verbal, and GMAT 111. He has also created explanations for problems in The Official Guide, as well as 1,800 practice GMAT math questions.

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